We investigate the presence of moral hazard and advantageous or adverse selection in a market for supplementary health insurance. For this we specify and estimate dynamic models for health insurance decisions and health care utilization. Estimates of the health care utilization models indicate that moral hazard is not important. Furthermore, we find strong evidence for advantageous selection, largely driven by heterogeneity in education, income and health preferences. Finally, we show that ignoring dynamics and unobserved fixed effects changes the results dramatically.